this has poyplexed me. it looks like the right cap prong goes into the middle pin of that tiny voltage regulator on the far right but the left pin i cant figure out. i think it goes into the bottom of the board into that blue thingy. i need to see how the circuit flows.
but yeah this is a common problem with me. the smaller a cap is the greater chance of the whole pad either coming off or solder lifting up. The cap fluid eats away at it making it very brittle. the 4.7 and the 33 uf caps are huge problems. of course the 100uf caps are biger and have more solder so no problem.
The best way for me to remove one of these caps is to use a small screwdriver and gently rock the cap back and forth where it gives way till it frictions off. if it leaves behind its old cap legs thats gold,easier to solder onto. flipping the motherboard to rest on the case makes it easier and wont harm it.
its takes about 15 to 20 minutes to rock it back and forth. it can move real fast like a blur but it gets boring but if you close your eyes and say the buddahist sutras the time will go fast.
i shape my caps legs for soldering first:
but apollo if the soldering welds are too tiny for you to do il do it for you for free. Solder paste or flux is like gold,makes tiny welds possible